Efficient mass-preserving finite volume approach for the rennet-induced coagulation equation

The coagulation of casein micelles caused by enzymes is a critical step in the dairy industry for cheese manufacture. During enzymatic coagulation of milk, three processes occur: enzymic proteolysis, coagulation, and gelation. This study presents the first numerical approach based on a finite volume scheme for describing the enzyme-induced coagulation of casein micelles. The finite volume scheme is mainly concerned with ensuring mass conservation and developed on the assumption that the particles are concentrated on the mean of each cell of the discretization. The key advantages of the new technique are its simple mathematical formulation and its robustness that allow it to be implemented on any type of grid and tailored to different coagulation kernels. The accuracy of the new approach is compared with newly derived analytical results for several gelling and non-gelling coagulation kernels. The comparison demonstrates that the new approach closely matches the exact results. In order to analyse the convergence behaviour of different order moments, various refined non-uniform grids have been taken into consideration.